Question

A monument is built out of toothpicks. There are 30 rows and each row has seven more toothpicks than the row above. The top row has five toothpicks. How many toothpicks are on the bottom row? Using complete sentences, explain the procedure taken to answer this question.

Answer 1

Which formula do I use to solve, please?

Answer 2

Each row increases the number of toothpicks by 7. How many times is the number of toothpicks increased?

Answer 3

30 times?

Answer 4

Close, you're on the right track. There are 30 rows total. The first has 5. How many times do we increase this by 7?

Answer 5

I'm not quite sure honestly, I just see "bottom row". can you give me a hint?

Answer 6

30 rows total. We're told the first row, so we don't count it.

Number of remaining rows: 29

Answer 7

Alright, so we increase 7 by 29, not including the first row

Answer 8

Right, so we can say that the bottom row has 7*29 more toothpicks than the top row. Just need to do one more little thing. What are we forgetting?

Answer 9

Should we multiply that by 5, since in the first row there are 5?

Answer 10

Not multiply, just add.

So, we start with 5, and the next 29 rows each increase by 7.

A given row has the number of toothpicks given by: 5+ 7*(row-1)

Answer 11

does this come to 208?

Answer 12

That's what I get :)

Does it all make sense?

Answer 13

Awesome! So this is the end of our solving? It makes sense to here, so is it my final answer

Answer 14

Yep

Answer 15

Thanks :D